Prefix code: Difference between revisions

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A '''prefix code''', also known as a '''prefix-free code''', '''comma-free code''' or '''instantaneous code''', is a [[code]] constructed so that dividing the code word into two pieces cannot result in the first being a code word. For example, the set {010,011,0,101} is not a prefix code because the entry '0' is the prefix of the entries 010 and 011. Hence, when receiving in series, 0101101, how do you know if it means 0,101,101 or 010,110,0, and so on. However, {01,101,110,0010} is a prefix code, because no entry is the start of any other entry.
 
This property permits the proper [[framing (telecommunication)|framing]] of transmitted code words when (a) external [[synchronization]] is provided to identify the start of the first code word in a [[sequence]] of code words and (b) no uncorrected errors occur in the symbol stream.
 
Examples of prefix codes are the variable-length [[Huffman coding|Huffman codes]], [[country calling codes]], [[ISBN]]s and the Secondary Synchronization Codes used in the [[UMTS]] [[W-CDMA]] 3G Wireless Standard.